The importance of including luck, probability and randomness in your financial decisions.
1 in 300,000. Those are the odds of you being killed by lightning, according to author David Hand in his book The Improbability Principle. What about getting lucky and hitting the jackpot in TOTO?
1 in 13,983,816.
[Free Ebook] How should you invest your first $20,000?
We asked 14 Singapore finance bloggers to share what they would do if they could go back in time and invest their first $20,000. They can no longer rewind time, but you can learn from their experience and hopefully start with a better footing.
You’re more likely to get struck by the wrath of Zeus than striking the grand prize in Singapore’s sanctioned lottery game. In spite of these long odds, thousands of people, young and old, regularly buy these papery pieces of hope, hoping to get lucky. In the long run, your expected return of investment is negative 36 percent. Essentially, for every dollar you invest in TOTO, you’re expected to get back 64 cents.
I can guarantee you though that if you present these numbers to a seasoned TOTO ticket buyer, he or she will still continue the habit, dismissing your concerns by chalking this purchase as an entertainment expense. The reason is part psychology and part emotion – it’s more unpleasant to lose S$100 at one go than to lose S$1 a hundred times. At the same time, the euphoria that their brains experience when they finally win a small amount clouds their judgement.
But, before you blame their irrationality, consider that emotions, irrational or otherwise, guide personal decisions, whole businesses, and even entire markets. In the seminal Descartes’ Error, neurologist and author Antonio Damasio argues that “the body and our emotions have a key role in the way we think and in rational decision-making”. Without emotions, and consequently irrationality, we would not be able to make a simple decision such as even getting out of bed without spending an inordinate amount of time weighing the possible consequences. (You could potentially die in a car crash if you get out of the comforts of your sheets!)
Emotions are the “lubricants of reason”. Our minds cease to function without them.
Being Irrational with Probability
Smart investors thrive and make money on irrationality. If markets were truly efficient and rational, no one would be making or losing money. The efficient-market hypothesis, which means that you cannot consistently achieve returns that beat market returns because all information is more or less available, has been hotly and publicly debated among the financial community.
The existence of a wide variety of bubbles – the tulip mania of 1637, the dot-com bubble at the turn of the millennium, the recent bitcoin craze, etc. – gives credence to the concept of irrationality in markets and the disproving of the efficient-market hypothesis. When the bubble bursts, in retrospect, our hindsight bias wonders why there were people silly enough to be in the bubble. Yet, most of the times, it’s almost impossible to detect that you’re in an over-inflated sphere until the soapy substance is all over yourself.
So, what does irrationality have to do with probability?
Our brains do not intuitively grasp probabilities. The famous Monty Hall problem, a conundrum that first appeared in 1990 in Marilyn vos Savant’s column in Parade magazine and one that befuddled mathematicians and statisticians alike, is the clearest example that our brains tend to fool us. The teaser was infuriatingly simple:
Suppose you’re on a game show, and you’re given the choice of three doors. Behind one is a car and behind the others, goats. You pick door 1 and the host, who knows what’s behind all the doors, opens door 3, which has a goat. He then says to you: “Do you want to pick door 2?” Is it to your advantage to switch your choice?
Intuitively, our mind tells us that switching doors wouldn’t make a difference because it will still be 50-50. However, as vos Savant proves in her detailed answer, it is advantageous to switch doors as you’ll have a 2/3 chance of winning the car as opposed to a 1/3 chance if you stay rooted to your choice.
According to psychologists, “people strongly tend to think probability is evenly distributed across as many unknowns as are present, whether it is or not”.
Probability Wears the Drapes of Luck
One of the most extreme examples of luck that I can think of is Russian roulette, a game of chance in which a single bullet is loaded into one of the six chambers in a revolver. The chamber is spun and the player brings the revolver to his temple before squeezing the trigger. Now, let’s up the ante – in a country starving for entertainment and devoid of censorship laws, a production company creates a game show revolving around Russian roulette. If you play the game and survive, you win a million dollars. If you lose, well, you lose your life. You have a 5 in 6 chance of walking away with money, and a 1 in 6 chance of dying. Clearly, this is a game of no skill and if you win, you will be given platitudes as a daring and bold risk taker. If you lose, you will be consigned to the footnotes of history.
Would you play the game?
Tens of thousands, if not tens of millions, of people play this game every day – the financial markets. While the risks are not as high (death or loss of limb is the ultimate deterrent; imagine if TOTO buyers had to give up a single finger for every purchase), the probability of financial ruin, disguised as a cataclysmic event, is still present. But, many don’t comprehend these probabilities and constantly take multiple risks when making investment decisions simply because they think that the one-in-a-million event will never occur.
When the markets perform, these people are lauded. When the opposite occurs, the sands of history slowly erode the lessons we gleaned from them and the cycle occurs again.
Remember how the chances of you winning TOTO is almost impossible? Yet, every year, there are multiple jackpot winners. It might seem like Father Luck has chosen them but it actually is just the laws of probability at play.
Probability in the Financial Markets
Similarly, in the financial markets, we also have to take into account the probability of a calamitous downturn when making our investment decisions (and whether we’re investing into a soapy, over-inflated bubble). Think about the Great Depression of 1929, the 1973 oil crisis, the 1997 Asian Financial Crisis, the 2007 – 2008 global financial crisis, etc. Each of these events have always been described as “unprecedented”, “unpredicted”, “never-before-seen”, etc. – basically a laundry list of adjectives that mean the same thing. Yet, if we apply the laws of probability to these seemingly random events, you would realise that it was only a matter of time before the numbers caught up to us. It might have been a one in a million chance, or perhaps a 1 in 13,983,816 chance, that the markets would crash into the depths.
But, as you can see from TOTO winners, or even from hundreds of other miraculous events and tragic disasters, it’s just a numbers game.
Recall the seasoned TOTO buyer and the psychology of losing a dollar in small incremental amounts and winning a large amount at one go. The same applies to making small, incremental amounts in the stock market, only to see it all wiped out in a single crash. The impact on our psyche can be catastrophic.
And with markets being as irrational and as populated as they currently are right now, and with the amount of emotions present as part of the human condition, it is always only a matter of time before another “unprecedented” huge decline occurs. You just need to be prepared for it.
So, you’ve got to ask yourself one question – “do I feel lucky?” Well, do ya?